Electrostatic contribution to the persistence length of a semiflexible dipolar chain

Conformational transitions and helical structures of a dipolar chain in external electric fields

The conformational behavior of a single dipolar chain in a uniform electric field is investigated by molecular dynamics simulations. The dipolar chain is modeled as a backbone bead-on-spring chain of equally charged beads, each connected by a rigid spring with an oppositely charged side bead that can freely rotate around the backbone bead. In the strong coupling regime, when the dipolar chain is in the globular state due to a strong electrostatic correlational attraction, the application of an electric field causes the chain swelling and elongation along the field direction. In the weak coupling regime, a qualitatively new regime is found when the swollen dipolar chain shrinks along the field direction adopting flattened conformations due to the field-induced anisotropy of the chain rigidity and the head-to-tail attraction of the dipoles orienting along the field lines. A novel helical conformation is detected for low-polar media and strong electric fields. An increasing rigidity of the backbone chain leads to some stabilization of the helical conformation and the formation of double and triple helices as well as flat spread springs. Fine tuning of the interplay between dipolar and volume interactions by external electric fields induces re-orientation of rod-like dipolar chains in dilute solutions. The obtained results can provide new ways to control dipolar polymer conformations and design materials with responsive properties.

An interplay of electrostatic and excluded volume interactions in the conformational behavior of a dipolar chain: theory and computer simulations

The effect of an interplay between electrostatic and excluded volume interactions on the conformational behavior of a dipolar chain has been studied theoretically and by means of molecular dynamics simulations. Every monomer unit of the dipolar chain comprises a dipole formed by a charged group of the chain and an oppositely charged counterion. The counterion is assumed to freely move around the chain but keeping the distance between oppositely charged ions (the dipole length) fixed. The novelty of the developed mean-field theory is that variations of the dipole parameters (the dipole length and the counterion size) have been accounted for in both electrostatic and excluded volume contributions to the total free energy of the dipolar chain. It has been shown that conformational transitions between swollen and collapsed states of the chain can be induced by fine-tuning the balance between electrostatic and excluded volume interactions. In particular, in low-polar media not only globule but also extended coil conformations can be realized even under strong electrostatic attraction. The results of MD simulations of a dipolar chain with variable dipolar length support theoretical conclusions.

Flory-type theories of polymer chains under different external stimuli

In this Review, we present a critical analysis of various applications of the Flory-type theories to a theoretical description of the conformational behavior of single polymer chains in dilute polymer solutions under a few external stimuli. Different theoretical models of flexible polymer chains in the supercritical fluid are discussed and analysed. Different points of view on the conformational behavior of the polymer chain near the liquid-gas transition critical point of the solvent are presented. A theoretical description of the co-solvent-induced coil-globule transitions within the implicit-solvent-explicit-co-solvent models is discussed. Several explicit-solvent-explicit-co-solvent theoretical models of the coil-to-globule-to-coil transition of the polymer chain in a mixture of good solvents (co-nonsolvency) are analysed and compared with each other. Finally, a new theoretical model of the conformational behavior of the dielectric polymer chain under the external constant electric field in the dilute polymer solution with an explicit account for the many-body dipole correlations is discussed. The polymer chain collapse induced by many-body dipole correlations of monomers in the context of statistical thermodynamics of dielectric polymers is analysed.

Statistical theory of polarizable target compound impregnation into a polymer coil under the influence of an electric field

The paper presents a theoretical approach for describing the influence of an electric field on the conformation of an electrically neutral dielectric polymer chain dissolved in a dielectric solvent with an admixture of a target compound. Each monomer and each molecule of the target compound carries positive excess polarizability and the solvent is described as a continuous dielectric medium. The model is based on the Flory-type mean-field theory. We demonstrate non-monotonic dependences of the expansion factor and the concentration of the target compound on the strength of the electric field and molecular polarizability. Namely, the target compound concentration in the internal polymer volume as a function of electric field strength has pronounced maxima if the molecules are polarizable. In addition, the expansion factor of the non-polarizable polymer chain can be controlled by the electric field. The dependences of the expansion factor and target compound concentration on the monomer polarizability exhibit minima and intersection points. The intersection points correspond to the equality of dielectric permittivities in the bulk solution and in the internal polymer volume.

Polymer chain collapse induced by many-body dipole correlations

We present a simple analytical theory of a flexible polymer chain dissolved in a good solvent, carrying permanent freely oriented dipoles on the monomers. We take into account the dipole correlations within the random phase approximation (RPA), as well as a dielectric heterogeneity in the internal polymer volume relative to the bulk solution. We demonstrate that the dipole correlations of monomers can be taken into account as pairwise ones only when the polymer chain is in a coil conformation. In this case the dipole correlations manifest themselves through the Keesom interactions of the permanent dipoles. On the other hand, the dielectric heterogeneity effect (dielectric mismatch effect) leads to the effective interaction between the monomers of the polymeric coil. Both of these effects can be taken into account by renormalizing the second virial coefficient of the monomer-monomer volume interactions. We establish that in the case when the solvent dielectric permittivity exceeds the dielectric permittivity of the polymeric material, the dielectric mismatch effect competes with the dipole attractive interactions, leading to polymer coil expansion. In the opposite case, both the dielectric mismatch effect and the dipole attractive interaction lead to the polymer coil collapse. We analyse the coil-globule transition caused by the dipole correlations of monomers within the many-body theory. We demonstrate that accounting for the dipole correlations higher than the pairwise ones smooths this pure electrostatics driven coil-globule transition of the polymer chain.

Polarizable polymer chain under external electric field: Effects of many-body electrostatic dipole correlations

We present a new simple self-consistent field theory of a polarizable flexible polymer chain under an external constant electric field with account for the many-body electrostatic dipole correlations. We show the effects of electrostatic dipole correlations on the electric-field-induced globule-coil transition. We demonstrate that only when the polymer chain is in the coil conformation, the electrostatic dipole correlations of monomers can be considered as pairwise. However, when the polymer chain is in a collapsed state, the dipole correlations have to be considered at the many-body level.

End-to-end distribution for a wormlike chain in arbitrary dimensions

We construct an efficient methodology for calculating wormlike chain statistics in arbitrary D dimensions over all chain rigidities, from fully rigid to completely flexible. The structure of our exact analytical solution for the end-to-end distribution function for a wormlike chain in arbitrary D dimensions in Fourier-Laplace space (i.e., Fourier-transformed end position and Laplace-transformed chain length) adopts the form of an infinite continued fraction, which is advantageous for its compact structure and stability for numerical implementation. We then proceed to present a step-by-step methodology for performing the Fourier-Laplace inversion in order to make full use of our results in general applications. Asymptotic methods for evaluating the Laplace inversion (power-law expansion and Rayleigh-Schrödinger perturbation theory) are employed in order to improve the accuracy of the numerical inversions of the end-to-end distribution function in real space. We adapt our results to the evaluation of the single-chain structure factor, rendering simple, closed-form expressions that facilitate comparison with scattering experiments. Using our techniques, the accuracy of the end-to-end distribution function is enhanced up to the limit of the machine precision. We demonstrate the utility of our methodology with realizations of the chain statistics, giving a general methodology that can be applied to a wide range of biophysical problems.